Fiber optical repeaters are used in a variety of applications where it is necessary to extend the distance over which an optical signal can be transimitted .some of the most common applications include : 

Telecommunications : fiber optical repeaters are used in long-distance teleommunications networks to amplify and regenerate optical signals . this allows signals to be transimitted over thousands of kilometers without losing too much of their strngth . 

Data centers : fiber optical repaters are used in data centers to connect different parts of the network.this allows for the efficient and reliable transmission of data between servers and other devices . 

Industrial automation : fiber optical repeaters are used in industrial automation systems to transmit control signals over long distances .this is necessary in applications where the physical distance between the controlloer and the actuator is too great for electrical signals to be used . 

Security systems : fiber optical repeaters are used in security systems to transmit video and audio signals over long distances .this is necessary for applications such as closed-circuit television (CCTV）and intrusion detection systems . 

In addition to those applications ,fiber optic repeaters are also used in a variety of the other industries ,such as healthcare , military ,and transportation . 

Here are some of the benifits of using fiber optical repeaters : 

They can extend the reach of optical signals over long distances . 

They can improve the quanlity of the optical signal by regenerating it . 

They are relatively small and easy to install .

They are reliable and have a long lifespan . 

Overall ,fiber optical repeaters are an essential component of many optical communication systems .they play a vital role in extending the reach and improving the quality of the optical signals .